# Compact Neural Networks based on the Multiscale Entanglement Renormalization Ansatz

arXiv: https://arxiv.org/abs/1711.03357 · HTML: https://mlsanity.com/paper/1711.03357/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2017.

## Built on by (most cited first, 3 of 3)

- [Efficient Visual Recognition with Deep Neural Networks: A Survey on Recent Advances and New Directions](https://mlsanity.com/paper/2108.13055/) (2021)
- [A Tensor Network Implementation of Multi Agent Reinforcement Learning](https://mlsanity.com/paper/2401.03896/) (2024)
- [Geometric Mean Pooling for Equal-Weight Multiplicative Coarse-Graining](https://mlsanity.com/paper/2609.21876/) (2026)

## Abstract (arXiv)

This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for the fully connected layers in a convolutional neural network and test this implementation on the CIFAR-10 and CIFAR-100 datasets. The proposed method outperforms factorization using tensor trains, providing greater compression for the same level of accuracy and greater accuracy for the same level of compression. We demonstrate MERA layers with 14000 times fewer parameters and a reduction in accuracy of less than 1% compared to the equivalent fully connected layers, scaling like O(N).